AN APPROXIMATION OF THE WAVE RUN-UP FREQUENCY DISTRIBUTION

Thorndike Saville

Abstract

The distribution of wave steepness (H/T ) for fully developed sea is obtained from Bretschneider's joint distribution of wave height and wave period. This steepness distribution is used with standard wave runup curves to develop a frequency curve of wave run-up. Use of this run-up distribution curve will permit more accurate estimation of the variability in wave run-up for design cases, and particularly the percent of time in which run-ups will exceed that predicted for the significant wave. The distribution may also be used with normal overtopping procedures to determine more accurate estimates of overtopping quantities. Wave run-up may be defined as the vertical height above mean water level to which water from a breaking wave will rise on a structure face. Accurate design data on the height of wave run-up is needed for determination of design crest elevations of protective structures subject to wave action such as seawalls, beach fills, surge barriers, and dams. Such structures are normally designed to prevent wave overtopping with consequent flooding on the landward side and, if of an earth type, possible failure by rearface erosion. Because of the importance of wave run-up elevations in determining structure heights and freeboards, a great deal of work has been done in the past six years in an attempt to relate wave run-up to incident wave characteristics, and slope or structure characteristics. Compilations based largely on laboratory experimental work have been made and have fe-?* suited in curves similar to those shown in Figure 1 which is reprinted from the U. S. Beach Erosion Board Technical Report No. 4. Such curves most frequently have related the dimensionless ratio of relative run-up (R/H ) to incident wave steepness in deep water (H /T ), as a function of structure type or slope. (H is the equivalent deep water wave height.) The curves shown in Figure 1 are of this type, and pertain to structures having a depth of water greater than three wave heights at the toe of the structure; this depth limitation in effect means that the wave breaks directly on the structure. The curves shown in Figure 1 are a portion of a set of five separate figures, covering different structure depths (d/H ). All are published in Beach Erosion Board Technical Report Number 4. These curves were derived primarily from small scale laboratory tests. Further laboratory tests with much larger waves (heights two to five feet) have shown that a scale effect exists for some conditions.